How would one coarsen a reference angle? It seems to me it would be very difficult to set an angle without being able to check it later to determine exactly what angle you ended up setting.

On the other hand, coarsening the detection would seem to mean using a detector with a large aperture so that when a detection is made, it will not be precisely where the particle was detected. Would that be a good example?

"We investigate the role of inefficiency in quantum measurements in the quantum-to-classical transition, and consistently observe the quantum-to-classical transition by coarsening the references of the measurements (e.g. when and where to measure). Our result suggests that the definition of measurement precision in quantum theory should include the degree of the observer's ability to precisely control the measurement references. "

This is perhaps the part that I least follow. It would seem to me that regardless of how well the reference was controlled, it would remain in the same state after the measurement so that it could be determined exactly what measurement had been made.

For example, let's say your control a an angle is a relatively fuzzy plus/minus 3 degrees. So you set to a target of 15 degrees, make the fuzzy measurement, and get the classical result. Then you go back and measure the angle and discover it is precisely 14.321 degrees. Why would you result be any different than if you were aiming for 14.321 degrees to begin with.

Obviously I am not interpreting their statement correctly. I'm hoping someone can explain the correct interpretation.